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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 46818.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 46818.d1 | 46818e3 | \([1, -1, 0, -311307, 66932549]\) | \(-189613868625/128\) | \(-2252324838528\) | \([]\) | \(211680\) | \(1.6860\) | |
| 46818.d2 | 46818e4 | \([1, -1, 0, -246282, 95624180]\) | \(-1159088625/2097152\) | \(-2989069302509862912\) | \([]\) | \(635040\) | \(2.2353\) | |
| 46818.d3 | 46818e2 | \([1, -1, 0, -12192, -539992]\) | \(-140625/8\) | \(-11402394495048\) | \([]\) | \(90720\) | \(1.2623\) | |
| 46818.d4 | 46818e1 | \([1, -1, 0, 813, -1585]\) | \(3375/2\) | \(-35192575602\) | \([]\) | \(30240\) | \(0.71302\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 46818.d have rank \(0\).
Complex multiplication
The elliptic curves in class 46818.d do not have complex multiplication.Modular form 46818.2.a.d
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.
\(\left(\begin{array}{rrrr} 1 & 3 & 21 & 7 \\ 3 & 1 & 7 & 21 \\ 21 & 7 & 1 & 3 \\ 7 & 21 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
